A massively parallel computation strategy for FDTD: time and space parallelism applied to electromagnetics problems

We present a novel strategy for incorporating massive parallelism into the solution of Maxwell's equations using finite-difference time-domain methods. In a departure from previous techniques wherein spatial parallelism is used, our approach exploits massive temporal parallelism by computing all of the time steps in parallel. Furthermore, in contrast to other methods which appear to concentrate on explicit schemes such as Yee's (1966) algorithm, our strategy uses the implicit Crank-Nicolson technique which provides superior numerical properties. We show that the use of temporal parallelism results in algorithms which offer a massive degree of coarse grain parallelism with minimum communication and synchronization requirements. Due to these features, the time-parallel algorithms are particularly suitable for implementation on emerging massively parallel multiple instruction-multiple data (MIMD) architectures. The methodology is applied to a circular cylindrical configuration, which serves as a testbed problem for the approach, to demonstrate the massive parallelism that can be exploited. We also discuss the generalization of the methodology for more complex problems.